Finite Group Databasebeta

← #29574006

Subgroups — #29574006

Order 15616.

612 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446006C212yesmaximal
2C2×#16839488C211yesmaximal, characteristic
3#21444072C211yesmaximal, characteristic
4#21443697C212yesmaximal
5C61×#2316C211yesmaximal, characteristic
6C22×C4⋊Dic61C2211yescharacteristic
7C2×#14519710—22no—
8C2×C22⋊#92418C2212yes—
9C2×#14519684—21no—
10C2×#14519684—21no—
11C2×#14519684C2211yescharacteristic
12#16839524—22no—
13#16839488C414yescomplemented
14C2×#117×C61—21no—
15C22×C4⋊C4×C61C2211yescharacteristic
16C61×#389—22no—
17C61×#389—22no—
18C61×#380—21no—
19C61×#380C2212yes—
20C23×Dic61—21no—
21C23×Dic61—21no—
22C22×#92418—22no—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61—42no—
25#14519710—44no—
26C22⋊#92418—22no—
27C22⋊#92418C2×C414yes—
28#14519684—22no—
29#14519684—42no—
30#14519684—42no—
31C23×C4×C61D411yescharacteristic
32C23×C4×C61D411yescharacteristic
33C23×C4×C61C2311yescharacteristic
34#117×C61—42no—
35#117×C61—42no—
36C2×C4⋊C4×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61C2×C412yes—
43C2×C4⋊C4×C61D412yes—
44C2×C4⋊C4×C61D412yes—
45C2×C4⋊C4×C61Q812yes—
46C2×C22⋊C4×C61—22no—
47C2×C42×C61—22no—
48#95×C61—22no—
49#95×C61—22no—
50C24×C61C2×D411yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—41no—
60C22×C4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61C4⋊C412yes—
64C22×C4×C61C4⋊C412yes—
65C22×C4×C61D812yes—
66C22×C4×C61Q1612yes—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D412yes—
69C22×C4×C61C2×Q811yescharacteristic
70C22×C4×C61#4112yes—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C4⋊C4×C61—24no—
86C4⋊C4×C61—24no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61—42no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—42no—
91C4⋊C4×C61—81no—
92C4⋊C4×C61—81no—
93C22⋊C4×C61—42no—
94C22⋊C4×C61—42no—
95C42×C61—44no—
96C4⋊Dic61—24no—
97C4⋊Dic61—42no—
98C2×#92418—24no—
99C2×#92418—42no—
100C2×#92418—42no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61C2×C4⋊C411yescharacteristic
106C23×C61#12011yescharacteristic
107C23×C61#12311yescharacteristic
108C23×C61C2×D811yescharacteristic
109C23×C61C2×Q1611yescharacteristic
110C23×C61AGL(1,ℤ/8)11yescharacteristic
111C23×C61#13711yescharacteristic
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61—22no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—81no—
134C2×C4×C61#10714yescomplemented
135C2×C4×C61C4×D412yes—
136C2×C4×C61C22⋊Q812yes—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151#92418—44no—
152#8856—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#38511yescharacteristic
166C22×C61C2×#10711yescharacteristic
167C22×C61#42811yescharacteristic
168C22×C61#44711yescharacteristic
169C22×C61#45111yescharacteristic
170C22×C61#45411yescharacteristic
171C22×C61#45611yescharacteristic
172C22×C61B(4,𝔽2)11yescharacteristic
173C22×C61#45811yescharacteristic
174C22×C61#48011yescharacteristic
175C22×C61#48411yescharacteristic
176C4×C61—24no—
177C4×C61—22no—
178C4×C61—22no—
179C4×C61—42no—
180C4×C61—82no—
181C4×C61—82no—
182Dic61—82no—
183Dic61—82no—
184#2316D6111yescharacteristic
185#1852—612no—
186C2×#324—611no—
187#1441—611no—
188#1294—612no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#159811yescharacteristic
194C2×C61#160511yescharacteristic
195C2×C61#161011yescharacteristic
196C2×C61#161711yescharacteristic
197C2×C61#185211yescharacteristic
198C2×C61#185711yescharacteristic
199C2×C61#186711yescharacteristic
200C2×#117—21no—
201C22×C4⋊C4—611no—
202C22×C4⋊C4C2×D6111yescharacteristic
203C2×#107—1222no—
204C2×C22⋊C8—612no—
205#389—22no—
206#389—22no—
207#380—21no—
208#380C2×D6112yes—
209C2×#95—611no—
210C2×#95—1221no—
211C2×#95—1221no—
212#340—1222no—
213#324—614no—
214C61#885611yescharacteristic, complemented, Sylow
215C23×C4—1221no—
216C23×C4—1221no—
217C23×C4C22⋊D6111yescharacteristic
218C23×C4C22⋊D6111yescharacteristic
219C23×C4C22×D6111yescharacteristic
220C22×C8—1222no—
221#117—42no—
222#117—42no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—1222no—
230C2×C4⋊C4—2442no—
231C2×C4⋊C4Dic12212yes—
232C2×C4⋊C4C4×D6112yes—
233C2×C4⋊C4C22⋊D6112yes—
234C2×C4⋊C4C22⋊D6112yes—
235C2×C22⋊C4—22no—
236C2×C42—22no—
237#107—2444no—
238C22⋊C8—614no—
239C22⋊C8—1222no—
240#95—22no—
241#95—22no—
242#95—1222no—
243#95—2442no—
244#95—2442no—
245C24C2×C22⋊D6111yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4#1175819612yes—
273C22×C4#1175819612yes—
274C22×C4#1175819912yes—
275C22×C4#1175820212yes—
276C22×C4C2×Dic12211yescharacteristic
277C22×C4C2×C4×D6111yescharacteristic
278C22×C4#1175822212yes—
279C22×C4C2×C22⋊D6112yes—
280C2×C8—1224no—
281C2×C8—2442no—
282C2×C8—2442no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—1224no—
292C4⋊C4—2442no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C42—44no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23C2×#1175819611yescharacteristic
301C23#1451974611yescharacteristic
302C23#1451976011yescharacteristic
303C23C2×#1175819911yescharacteristic
304C23C2×#1175820211yescharacteristic
305C23#1451980311yescharacteristic
306C23#1451980811yescharacteristic
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4#1451971014yescomplemented
344C2×C4C4×C22⋊D6112yes—
345C2×C4#1451975612yes—
346C8—2444no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#1683963511yescharacteristic
360C22C2×#1451971011yescharacteristic
361C22#1683980211yescharacteristic
362C22#1683989611yescharacteristic
363C22#1683991811yescharacteristic
364C22#1683993511yescharacteristic
365C22#1683994511yescharacteristic
366C22#1683994911yescharacteristic
367C22#1683995211yescharacteristic
368C22#1684007511yescharacteristic
369C22#1684009711yescharacteristic
370C4—24no—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4—4882no—
377C4—4882no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#2144475411yescharacteristic
383C2#2144479311yescharacteristic
384C2#2144482211yescharacteristic
385C2#2144486111yescharacteristic
386C2#2144600711yescharacteristic
387C2#2144603411yescharacteristic
388C2#2144610011yescharacteristic
subgroupG/H
centerC23#14519746
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2316C2
socleC23×C61#120
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#2316D61
hypocenterC61#8856
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2316

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
13. #16839488C4semidirect
134. C2×C4×C61#107semidirect
214. C61#8856semidirect
343. C2×C4#14519710semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214460062
C2×#168394882
#214440722
#214436972
C61×#23162
#885661